sinatras/pmpp-eval huggingface dataset:
Task: ch20-stencil-25pt-slab-stage2-interior
Target file: student_kernel.cu

Goal: Implement the Stage-2 interior pass for the 3D 25-point stencil. This pass updates only the interior owned planes (excluding the four boundary planes already handled in Stage-1).

Key requirements:
- Owned region indices: `[4 .. 4+dimz-1]`; Stage-2 updates planes `k  [8 .. 4+dimz-5]`.
- Use the same stencil weights (w0..w4) applied to 1..4 offsets in each dimension.
- Respect copy-through behaviour near x/y faces inside the interior range.
- Write nothing outside the designated interior planes.

Skeleton:
```cuda
#include <cuda_runtime.h>

// TODO: Implement Stage-2 interior update for the 25-point stencil (R=4).
// Local z extent = dimz + 8. Owned z = [4 .. 4+dimz-1].
// Stage-2 interior planes: k  [8 .. (4+dimz-1)-4].
// For i/j edges (i<4 || i>=dimx-4 || j<4 || j>=dimy-4) copy-through.
// Do not touch halos or Stage-1 planes.
//
// STENCIL WEIGHTS: Use distance-based weighted stencil (NOT simple averaging!)
// - w0 = 0.5   (center point)
// - w1 = 0.10  (distance 1 neighbors: 1 in each axis)
// - w2 = 0.05  (distance 2 neighbors: 2 in each axis)
// - w3 = 0.025 (distance 3 neighbors: 3 in each axis)
// - w4 = 0.0125 (distance 4 neighbors: 4 in each axis)
//
// Formula: out[i,j,k] = w0 * in[i,j,k]
//                     + w1 * (in[i1,j,k] + in[i,j1,k] + in[i,j,k1])
//                     + w2 * (in[i2,j,k] + in[i,j2,k] + in[i,j,k2])
//                     + w3 * (in[i3,j,k] + in[i,j3,k] + in[i,j,k3])
//                     + w4 * (in[i4,j,k] + in[i,j4,k] + in[i,j,k4])

static inline __device__ size_t idx3(int i,int j,int k,int dx,int dy){
    return (size_t(k)*dy + j)*dx + i;
}

__global__ void stencil25_stage2_kernel(const float* __restrict__ in,
                                        float* __restrict__ out,
                                        int dimx,int dimy,int dimz)
{
    // TODO
}

extern "C" void stencil25_stage2_interior(const float* d_in, float* d_out,
                                          int dimx,int dimy,int dimz)
{
    // TODO: launch 3D grid and synchronize
}
```
Task: ch21-bezier-dp-parent-child-single
Target file: student_kernel.cu

Here is the current skeleton you must complete:

```cuda
// ch21-bezier-dp-parent-child-single / student_kernel.cu
#include <cuda_runtime.h>
#include <stdint.h>

// Use CUDA builtin float2
#include <vector_types.h>

struct BezierLine {
  float2 CP[3];        // P0, P1, P2
  float2* vertexPos;   // device buffer (allocated in parent via device malloc)
  int     nVertices;   // chosen per line in parent
};

// --- You implement these -----------------------------------------------------

// Geometric curvature proxy: distance from P1 to line P0-P2 (normalized by |P2-P0|)
// Return non-negative curvature (0 for degenerate segment).
__device__ float curvature_of(const float2 P0, const float2 P1, const float2 P2) {
  // TODO: implement robust point-to-segment distance proxy.
  // Hints:
  //   v = P2 - P0
  //   w = P1 - P0
  //   area2 = |v.x*w.y - v.y*w.x|     (2x triangle area)
  //   base  = sqrt(v.x*v.x + v.y*v.y)
  //   curvature ~ area2 / max(base, 1e-8)
  return 0.0f; // TODO
}

// Child kernel: compute tessellated positions for one line lidx.
__global__ void computeBezierLine_child(int lidx, BezierLine* bLines, int nTess) {
  // TODO:
  //  - idx = blockIdx.x*blockDim.x + threadIdx.x
  //  - if idx >= nTess: return
  //  - u = idx / (nTess-1)   (float)
  //  - B0=(1-u)^2, B1=2u(1-u), B2=u^2
  //  - position = B0*P0 + B1*P1 + B2*P2
  //  - write to bLines[lidx].vertexPos[idx]
}

// Parent kernel: choose tessellation density, allocate vertex buffers, launch child.
__global__ void computeBezierLines_parent(BezierLine* bLines, int nLines, int maxTess) {
  // TODO:
  //  - lidx = blockIdx.x*blockDim.x + threadIdx.x; if (lidx>=nLines) return
  //  - compute curvature_of(...)
  //  - nVerts = clamp( int(curv*16.f)+4, 4, maxTess );
  //  - bLines[lidx].nVertices = nVerts;
  //  - bLines[lidx].vertexPos = (float2*)malloc(nVerts * sizeof(float2));
  //      * if malloc returns nullptr, set nVertices=0 and return.
  //  - launch child: <<< (nVerts+31)/32, 32 >>> computeBezierLine_child(lidx, bLines, nVerts);
}
```
Task: ch21-bezier-dp-free-child-buffers
Target file: student_kernel.cu

Here is the current skeleton you must complete:

```cuda
// ch21-bezier-dp-free-child-buffers / student_kernel.cu
#include <cuda_runtime.h>
#include <stdint.h>

#include <vector_types.h>

struct BezierLine {
  float2 CP[3];
  float2* vertexPos; // device-heap pointer
  int     nVertices;
};

// TODO: Implement idempotent free:
//  - lidx = blockIdx.x*blockDim.x + threadIdx.x; if (lidx>=nLines) return;
//  - if (bLines[lidx].vertexPos != nullptr) { free(ptr); bLines[lidx].vertexPos = nullptr; }
//  - (optional) bLines[lidx].nVertices = 0;
__global__ void freeVertexMem(BezierLine* bLines, int nLines) {
  // TODO
}
```
Task: ch21-quadtree-dp-pack-coalesced
            Target file: student_kernel.cu

            Implementation requirements:
- Use shared memory arrays to track counts, offsets, and cursors for four quadrants.
- Count the number of indices per quadrant within the segment.
- Compute exclusive offsets in NW, NE, SW, SE order.
- Scatter indices back into idx_out[segBegin:segBegin+segCount) with stable ordering within each quadrant.

            Here is the current student_kernel.cu:

            ```cuda
            // ch21-quadtree-dp-pack-coalesced / student_kernel.cu
#include <cuda_runtime.h>
#include <stdint.h>

// TODO: Implement quadrant classification helpers
// Each function should determine if point (px, py) belongs to the specified quadrant
// of the bounding box [minx, miny, maxx, maxy].
//
// Hints:
// - Compute midpoint: mx = (minx + maxx) / 2, my = (miny + maxy) / 2
// - NW (Northwest): px < mx AND py >= my
// - NE (Northeast): px >= mx AND py >= my
// - SW (Southwest): px < mx AND py < my
// - SE (Southeast): px >= mx AND py < my

extern "C" __global__
void pack_quadrants_singleblock(const float* __restrict__ x,
                                const float* __restrict__ y,
                                const int*   __restrict__ idx_in,
                                int*         __restrict__ idx_out,
                                int segBegin, int segCount,
                                float minx, float miny, float maxx, float maxy)
{
  // TODO: Implement quadrant packing with shared memory count/scan/scatter:
  //
  // Step 1: Count phase
  // - Each thread classifies its assigned points into one of 4 quadrants
  // - Use your quadrant helper functions (in_NW, in_NE, in_SW, in_SE)
  // - Store per-thread counts for each quadrant in shared memory
  //
  // Step 2: Parallel scan (prefix sum)
  // - Compute exclusive scan of counts for each quadrant to get write offsets
  // - This ensures stable ordering (preserves input order within each quadrant)
  // - Use __syncthreads() between phases
  //
  // Step 3: Scatter phase
  // - Each thread writes its assigned points to idx_out at computed offsets
  // - NW quadrant: starts at offset 0
  // - NE quadrant: starts at offset count_NW
  // - SW quadrant: starts at offset count_NW + count_NE
  // - SE quadrant: starts at offset count_NW + count_NE + count_SW
  //
  // Hints:
  // - Single block kernel: use blockDim.x threads
  // - Shared memory arrays for counts and offsets
  // - Points are indexed via idx_in[segBegin + i]
  // - Point coordinates: x[idx], y[idx]
  (void)x; (void)y; (void)idx_in; (void)idx_out;
  (void)segBegin; (void)segCount;
  (void)minx; (void)miny; (void)maxx; (void)maxy;
}
            ```